Clamping devices for removable mounting of tools or tool fixtures in a receiving part generally have a collet chuck arranged in the receiving part, or a clamping set with several pincer elements distributed around the periphery to engage with the tool or tool fixture. In conventional clamping devices, the pincer elements are generally arranged on an axially movable mount or they are activated by an axially displaced clamping cone. In both designs, however, relatively large axial displacements or travel movements of the pincer mount or the clamping cone are required to move the pincer elements between a clamping and a releasing position. Since these travel movements usually occur against the force of a clamping spring when loosening the collet chuck, a relatively high expenditure of force and energy is thereby required. Furthermore, an appropriately large design space must be provided for the necessary travel movements.